Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
566 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14544701 | C2 | semidirect |
| 2. C4×#10587544 | C2 | semidirect |
| 3. #14543601 | C2 | semidirect |
| 212. C17 | #7659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544701 | 2 |
| C4×#10587544 | 2 |
| #14543601 | 2 |
| #14537142 | 2 |
| #7659 | 17 |